Create model class for AI4PDE

[lm2612]

Issue

Move class AI4CFD from script into a source code class. We may want to create a base class for a general class and then have classes inherit from this for each different case (advection diffusion, 2D Navier Stokes, 3D Navier Stokes). One question to address is how general should the base class be - we want to avoid repeating code.

We want to the call the model as something like: model = NavierStokes2D(grid, ...)

• initialize it as simulation = model.initialize()
• then run it as simulation = simulation.run(n_timesteps). Inside this we will call model.forward(...)

Simulation contains prognostic variables, diagnostic variables and model

Thoughts

Similarities/differences

• The 2D classes share similar __init__.
• Navier Stokes solvers both use similar F_cycle_MG but this depends on the boundary conditions (whether 2D or 3D).

Currently we have think there are three components that could be separated:

• Numerical methods
• Boundary conditions
• The model itself (user will have to define forward)

[lm2612]

For ideas on how to address this, we will compare against other PDE solver packages. These might be relevant:

https://github.com/zwicker-group/py-pde
https://github.com/sympy/sympy/tree/master https://github.com/firedrakeproject/firedrake https://github.com/usnistgov/fipy https://github.com/tum-pbs/PhiFlow/tree/master https://github.com/mcgibbon/sympl/tree/master https://github.com/CliMT/climt/tree/develop

julia https://github.com/SpeedyWeather/SpeedyWeather.jl https://github.com/CliMA/Oceananigans.jl